Prologue General relativity is a beautiful scheme for describing the gravitational �eld and the equations it obeys. Nowadays this theory is often used as a prototype for other, more intricate constructions to describe forces between elementary particles or other branches of fundamental physics. This is why in an introduction to general relativity it is of importance to separate as clearly as possible the various ingredients that together give shape to this paradigm. After explaining the physical motivations we �rst introduce curved coordinates, then add to this the notion of an a_ne connection �eld and only as a later step add to that the metric �eld. One then sees clearly how space and time get more and more structure, until �nally all we have to do is deduce Einstein�s �eld equations.